/*
 * Copyright (c) 1997, 2011, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

package java.awt.geom;

import java.awt.Shape;
import java.awt.Rectangle;
import java.util.Arrays;
import java.io.Serializable;
import sun.awt.geom.Curve;

import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.ulp;

/**
 * The <code>CubicCurve2D</code> class defines a cubic parametric curve
 * segment in {@code (x,y)} coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects which
 * store a 2D cubic curve segment.
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @author Jim Graham
 * @since 1.2
 */
public abstract class CubicCurve2D implements Shape, Cloneable {

  /**
   * A cubic parametric curve segment specified with
   * {@code float} coordinates.
   *
   * @since 1.2
   */
  public static class Float extends CubicCurve2D implements Serializable {

    /**
     * The X coordinate of the start point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float x1;

    /**
     * The Y coordinate of the start point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float y1;

    /**
     * The X coordinate of the first control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrlx1;

    /**
     * The Y coordinate of the first control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrly1;

    /**
     * The X coordinate of the second control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrlx2;

    /**
     * The Y coordinate of the second control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float ctrly2;

    /**
     * The X coordinate of the end point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float x2;

    /**
     * The Y coordinate of the end point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public float y2;

    /**
     * Constructs and initializes a CubicCurve with coordinates
     * (0, 0, 0, 0, 0, 0, 0, 0).
     *
     * @since 1.2
     */
    public Float() {
    }

    /**
     * Constructs and initializes a {@code CubicCurve2D} from
     * the specified {@code float} coordinates.
     *
     * @param x1 the X coordinate for the start point of the resulting {@code CubicCurve2D}
     * @param y1 the Y coordinate for the start point of the resulting {@code CubicCurve2D}
     * @param ctrlx1 the X coordinate for the first control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrly1 the Y coordinate for the first control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrlx2 the X coordinate for the second control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrly2 the Y coordinate for the second control point of the resulting {@code
     * CubicCurve2D}
     * @param x2 the X coordinate for the end point of the resulting {@code CubicCurve2D}
     * @param y2 the Y coordinate for the end point of the resulting {@code CubicCurve2D}
     * @since 1.2
     */
    public Float(float x1, float y1,
        float ctrlx1, float ctrly1,
        float ctrlx2, float ctrly2,
        float x2, float y2) {
      setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX1() {
      return (double) x1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY1() {
      return (double) y1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP1() {
      return new Point2D.Float(x1, y1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX1() {
      return (double) ctrlx1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY1() {
      return (double) ctrly1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlP1() {
      return new Point2D.Float(ctrlx1, ctrly1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX2() {
      return (double) ctrlx2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY2() {
      return (double) ctrly2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlP2() {
      return new Point2D.Float(ctrlx2, ctrly2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX2() {
      return (double) x2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY2() {
      return (double) y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP2() {
      return new Point2D.Float(x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public void setCurve(double x1, double y1,
        double ctrlx1, double ctrly1,
        double ctrlx2, double ctrly2,
        double x2, double y2) {
      this.x1 = (float) x1;
      this.y1 = (float) y1;
      this.ctrlx1 = (float) ctrlx1;
      this.ctrly1 = (float) ctrly1;
      this.ctrlx2 = (float) ctrlx2;
      this.ctrly2 = (float) ctrly2;
      this.x2 = (float) x2;
      this.y2 = (float) y2;
    }

    /**
     * Sets the location of the end points and control points
     * of this curve to the specified {@code float} coordinates.
     *
     * @param x1 the X coordinate used to set the start point of this {@code CubicCurve2D}
     * @param y1 the Y coordinate used to set the start point of this {@code CubicCurve2D}
     * @param ctrlx1 the X coordinate used to set the first control point of this {@code
     * CubicCurve2D}
     * @param ctrly1 the Y coordinate used to set the first control point of this {@code
     * CubicCurve2D}
     * @param ctrlx2 the X coordinate used to set the second control point of this {@code
     * CubicCurve2D}
     * @param ctrly2 the Y coordinate used to set the second control point of this {@code
     * CubicCurve2D}
     * @param x2 the X coordinate used to set the end point of this {@code CubicCurve2D}
     * @param y2 the Y coordinate used to set the end point of this {@code CubicCurve2D}
     * @since 1.2
     */
    public void setCurve(float x1, float y1,
        float ctrlx1, float ctrly1,
        float ctrlx2, float ctrly2,
        float x2, float y2) {
      this.x1 = x1;
      this.y1 = y1;
      this.ctrlx1 = ctrlx1;
      this.ctrly1 = ctrly1;
      this.ctrlx2 = ctrlx2;
      this.ctrly2 = ctrly2;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Rectangle2D getBounds2D() {
      float left = Math.min(Math.min(x1, x2),
          Math.min(ctrlx1, ctrlx2));
      float top = Math.min(Math.min(y1, y2),
          Math.min(ctrly1, ctrly2));
      float right = Math.max(Math.max(x1, x2),
          Math.max(ctrlx1, ctrlx2));
      float bottom = Math.max(Math.max(y1, y2),
          Math.max(ctrly1, ctrly2));
      return new Rectangle2D.Float(left, top,
          right - left, bottom - top);
    }

    /*
     * JDK 1.6 serialVersionUID
     */
    private static final long serialVersionUID = -1272015596714244385L;
  }

  /**
   * A cubic parametric curve segment specified with
   * {@code double} coordinates.
   *
   * @since 1.2
   */
  public static class Double extends CubicCurve2D implements Serializable {

    /**
     * The X coordinate of the start point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double x1;

    /**
     * The Y coordinate of the start point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double y1;

    /**
     * The X coordinate of the first control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrlx1;

    /**
     * The Y coordinate of the first control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrly1;

    /**
     * The X coordinate of the second control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrlx2;

    /**
     * The Y coordinate of the second control point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double ctrly2;

    /**
     * The X coordinate of the end point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double x2;

    /**
     * The Y coordinate of the end point
     * of the cubic curve segment.
     *
     * @serial
     * @since 1.2
     */
    public double y2;

    /**
     * Constructs and initializes a CubicCurve with coordinates
     * (0, 0, 0, 0, 0, 0, 0, 0).
     *
     * @since 1.2
     */
    public Double() {
    }

    /**
     * Constructs and initializes a {@code CubicCurve2D} from
     * the specified {@code double} coordinates.
     *
     * @param x1 the X coordinate for the start point of the resulting {@code CubicCurve2D}
     * @param y1 the Y coordinate for the start point of the resulting {@code CubicCurve2D}
     * @param ctrlx1 the X coordinate for the first control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrly1 the Y coordinate for the first control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrlx2 the X coordinate for the second control point of the resulting {@code
     * CubicCurve2D}
     * @param ctrly2 the Y coordinate for the second control point of the resulting {@code
     * CubicCurve2D}
     * @param x2 the X coordinate for the end point of the resulting {@code CubicCurve2D}
     * @param y2 the Y coordinate for the end point of the resulting {@code CubicCurve2D}
     * @since 1.2
     */
    public Double(double x1, double y1,
        double ctrlx1, double ctrly1,
        double ctrlx2, double ctrly2,
        double x2, double y2) {
      setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX1() {
      return x1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY1() {
      return y1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP1() {
      return new Point2D.Double(x1, y1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX1() {
      return ctrlx1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY1() {
      return ctrly1;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlP1() {
      return new Point2D.Double(ctrlx1, ctrly1);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlX2() {
      return ctrlx2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getCtrlY2() {
      return ctrly2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getCtrlP2() {
      return new Point2D.Double(ctrlx2, ctrly2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getX2() {
      return x2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public double getY2() {
      return y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Point2D getP2() {
      return new Point2D.Double(x2, y2);
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public void setCurve(double x1, double y1,
        double ctrlx1, double ctrly1,
        double ctrlx2, double ctrly2,
        double x2, double y2) {
      this.x1 = x1;
      this.y1 = y1;
      this.ctrlx1 = ctrlx1;
      this.ctrly1 = ctrly1;
      this.ctrlx2 = ctrlx2;
      this.ctrly2 = ctrly2;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * {@inheritDoc}
     *
     * @since 1.2
     */
    public Rectangle2D getBounds2D() {
      double left = Math.min(Math.min(x1, x2),
          Math.min(ctrlx1, ctrlx2));
      double top = Math.min(Math.min(y1, y2),
          Math.min(ctrly1, ctrly2));
      double right = Math.max(Math.max(x1, x2),
          Math.max(ctrlx1, ctrlx2));
      double bottom = Math.max(Math.max(y1, y2),
          Math.max(ctrly1, ctrly2));
      return new Rectangle2D.Double(left, top,
          right - left, bottom - top);
    }

    /*
     * JDK 1.6 serialVersionUID
     */
    private static final long serialVersionUID = -4202960122839707295L;
  }

  /**
   * This is an abstract class that cannot be instantiated directly.
   * Type-specific implementation subclasses are available for
   * instantiation and provide a number of formats for storing
   * the information necessary to satisfy the various accessor
   * methods below.
   *
   * @see java.awt.geom.CubicCurve2D.Float
   * @see java.awt.geom.CubicCurve2D.Double
   * @since 1.2
   */
  protected CubicCurve2D() {
  }

  /**
   * Returns the X coordinate of the start point in double precision.
   *
   * @return the X coordinate of the start point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getX1();

  /**
   * Returns the Y coordinate of the start point in double precision.
   *
   * @return the Y coordinate of the start point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getY1();

  /**
   * Returns the start point.
   *
   * @return a {@code Point2D} that is the start point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract Point2D getP1();

  /**
   * Returns the X coordinate of the first control point in double precision.
   *
   * @return the X coordinate of the first control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getCtrlX1();

  /**
   * Returns the Y coordinate of the first control point in double precision.
   *
   * @return the Y coordinate of the first control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getCtrlY1();

  /**
   * Returns the first control point.
   *
   * @return a {@code Point2D} that is the first control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract Point2D getCtrlP1();

  /**
   * Returns the X coordinate of the second control point
   * in double precision.
   *
   * @return the X coordinate of the second control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getCtrlX2();

  /**
   * Returns the Y coordinate of the second control point
   * in double precision.
   *
   * @return the Y coordinate of the second control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getCtrlY2();

  /**
   * Returns the second control point.
   *
   * @return a {@code Point2D} that is the second control point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract Point2D getCtrlP2();

  /**
   * Returns the X coordinate of the end point in double precision.
   *
   * @return the X coordinate of the end point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getX2();

  /**
   * Returns the Y coordinate of the end point in double precision.
   *
   * @return the Y coordinate of the end point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract double getY2();

  /**
   * Returns the end point.
   *
   * @return a {@code Point2D} that is the end point of the {@code CubicCurve2D}.
   * @since 1.2
   */
  public abstract Point2D getP2();

  /**
   * Sets the location of the end points and control points of this curve
   * to the specified double coordinates.
   *
   * @param x1 the X coordinate used to set the start point of this {@code CubicCurve2D}
   * @param y1 the Y coordinate used to set the start point of this {@code CubicCurve2D}
   * @param ctrlx1 the X coordinate used to set the first control point of this {@code
   * CubicCurve2D}
   * @param ctrly1 the Y coordinate used to set the first control point of this {@code
   * CubicCurve2D}
   * @param ctrlx2 the X coordinate used to set the second control point of this {@code
   * CubicCurve2D}
   * @param ctrly2 the Y coordinate used to set the second control point of this {@code
   * CubicCurve2D}
   * @param x2 the X coordinate used to set the end point of this {@code CubicCurve2D}
   * @param y2 the Y coordinate used to set the end point of this {@code CubicCurve2D}
   * @since 1.2
   */
  public abstract void setCurve(double x1, double y1,
      double ctrlx1, double ctrly1,
      double ctrlx2, double ctrly2,
      double x2, double y2);

  /**
   * Sets the location of the end points and control points of this curve
   * to the double coordinates at the specified offset in the specified
   * array.
   *
   * @param coords a double array containing coordinates
   * @param offset the index of <code>coords</code> from which to begin setting the end points and
   * control points of this curve to the coordinates contained in <code>coords</code>
   * @since 1.2
   */
  public void setCurve(double[] coords, int offset) {
    setCurve(coords[offset + 0], coords[offset + 1],
        coords[offset + 2], coords[offset + 3],
        coords[offset + 4], coords[offset + 5],
        coords[offset + 6], coords[offset + 7]);
  }

  /**
   * Sets the location of the end points and control points of this curve
   * to the specified <code>Point2D</code> coordinates.
   *
   * @param p1 the first specified <code>Point2D</code> used to set the start point of this curve
   * @param cp1 the second specified <code>Point2D</code> used to set the first control point of
   * this curve
   * @param cp2 the third specified <code>Point2D</code> used to set the second control point of
   * this curve
   * @param p2 the fourth specified <code>Point2D</code> used to set the end point of this curve
   * @since 1.2
   */
  public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
    setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
        cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
  }

  /**
   * Sets the location of the end points and control points of this curve
   * to the coordinates of the <code>Point2D</code> objects at the specified
   * offset in the specified array.
   *
   * @param pts an array of <code>Point2D</code> objects
   * @param offset the index of <code>pts</code> from which to begin setting the end points and
   * control points of this curve to the points contained in <code>pts</code>
   * @since 1.2
   */
  public void setCurve(Point2D[] pts, int offset) {
    setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
        pts[offset + 1].getX(), pts[offset + 1].getY(),
        pts[offset + 2].getX(), pts[offset + 2].getY(),
        pts[offset + 3].getX(), pts[offset + 3].getY());
  }

  /**
   * Sets the location of the end points and control points of this curve
   * to the same as those in the specified <code>CubicCurve2D</code>.
   *
   * @param c the specified <code>CubicCurve2D</code>
   * @since 1.2
   */
  public void setCurve(CubicCurve2D c) {
    setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
        c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
  }

  /**
   * Returns the square of the flatness of the cubic curve specified
   * by the indicated control points. The flatness is the maximum distance
   * of a control point from the line connecting the end points.
   *
   * @param x1 the X coordinate that specifies the start point of a {@code CubicCurve2D}
   * @param y1 the Y coordinate that specifies the start point of a {@code CubicCurve2D}
   * @param ctrlx1 the X coordinate that specifies the first control point of a {@code
   * CubicCurve2D}
   * @param ctrly1 the Y coordinate that specifies the first control point of a {@code
   * CubicCurve2D}
   * @param ctrlx2 the X coordinate that specifies the second control point of a {@code
   * CubicCurve2D}
   * @param ctrly2 the Y coordinate that specifies the second control point of a {@code
   * CubicCurve2D}
   * @param x2 the X coordinate that specifies the end point of a {@code CubicCurve2D}
   * @param y2 the Y coordinate that specifies the end point of a {@code CubicCurve2D}
   * @return the square of the flatness of the {@code CubicCurve2D} represented by the specified
   * coordinates.
   * @since 1.2
   */
  public static double getFlatnessSq(double x1, double y1,
      double ctrlx1, double ctrly1,
      double ctrlx2, double ctrly2,
      double x2, double y2) {
    return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
        Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));

  }

  /**
   * Returns the flatness of the cubic curve specified
   * by the indicated control points. The flatness is the maximum distance
   * of a control point from the line connecting the end points.
   *
   * @param x1 the X coordinate that specifies the start point of a {@code CubicCurve2D}
   * @param y1 the Y coordinate that specifies the start point of a {@code CubicCurve2D}
   * @param ctrlx1 the X coordinate that specifies the first control point of a {@code
   * CubicCurve2D}
   * @param ctrly1 the Y coordinate that specifies the first control point of a {@code
   * CubicCurve2D}
   * @param ctrlx2 the X coordinate that specifies the second control point of a {@code
   * CubicCurve2D}
   * @param ctrly2 the Y coordinate that specifies the second control point of a {@code
   * CubicCurve2D}
   * @param x2 the X coordinate that specifies the end point of a {@code CubicCurve2D}
   * @param y2 the Y coordinate that specifies the end point of a {@code CubicCurve2D}
   * @return the flatness of the {@code CubicCurve2D} represented by the specified coordinates.
   * @since 1.2
   */
  public static double getFlatness(double x1, double y1,
      double ctrlx1, double ctrly1,
      double ctrlx2, double ctrly2,
      double x2, double y2) {
    return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
        ctrlx2, ctrly2, x2, y2));
  }

  /**
   * Returns the square of the flatness of the cubic curve specified
   * by the control points stored in the indicated array at the
   * indicated index. The flatness is the maximum distance
   * of a control point from the line connecting the end points.
   *
   * @param coords an array containing coordinates
   * @param offset the index of <code>coords</code> from which to begin getting the end points and
   * control points of the curve
   * @return the square of the flatness of the <code>CubicCurve2D</code> specified by the
   * coordinates in <code>coords</code> at the specified offset.
   * @since 1.2
   */
  public static double getFlatnessSq(double coords[], int offset) {
    return getFlatnessSq(coords[offset + 0], coords[offset + 1],
        coords[offset + 2], coords[offset + 3],
        coords[offset + 4], coords[offset + 5],
        coords[offset + 6], coords[offset + 7]);
  }

  /**
   * Returns the flatness of the cubic curve specified
   * by the control points stored in the indicated array at the
   * indicated index.  The flatness is the maximum distance
   * of a control point from the line connecting the end points.
   *
   * @param coords an array containing coordinates
   * @param offset the index of <code>coords</code> from which to begin getting the end points and
   * control points of the curve
   * @return the flatness of the <code>CubicCurve2D</code> specified by the coordinates in
   * <code>coords</code> at the specified offset.
   * @since 1.2
   */
  public static double getFlatness(double coords[], int offset) {
    return getFlatness(coords[offset + 0], coords[offset + 1],
        coords[offset + 2], coords[offset + 3],
        coords[offset + 4], coords[offset + 5],
        coords[offset + 6], coords[offset + 7]);
  }

  /**
   * Returns the square of the flatness of this curve.  The flatness is the
   * maximum distance of a control point from the line connecting the
   * end points.
   *
   * @return the square of the flatness of this curve.
   * @since 1.2
   */
  public double getFlatnessSq() {
    return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
        getCtrlX2(), getCtrlY2(), getX2(), getY2());
  }

  /**
   * Returns the flatness of this curve.  The flatness is the
   * maximum distance of a control point from the line connecting the
   * end points.
   *
   * @return the flatness of this curve.
   * @since 1.2
   */
  public double getFlatness() {
    return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
        getCtrlX2(), getCtrlY2(), getX2(), getY2());
  }

  /**
   * Subdivides this cubic curve and stores the resulting two
   * subdivided curves into the left and right curve parameters.
   * Either or both of the left and right objects may be the same
   * as this object or null.
   *
   * @param left the cubic curve object for storing for the left or first half of the subdivided
   * curve
   * @param right the cubic curve object for storing for the right or second half of the subdivided
   * curve
   * @since 1.2
   */
  public void subdivide(CubicCurve2D left, CubicCurve2D right) {
    subdivide(this, left, right);
  }

  /**
   * Subdivides the cubic curve specified by the <code>src</code> parameter
   * and stores the resulting two subdivided curves into the
   * <code>left</code> and <code>right</code> curve parameters.
   * Either or both of the <code>left</code> and <code>right</code> objects
   * may be the same as the <code>src</code> object or <code>null</code>.
   *
   * @param src the cubic curve to be subdivided
   * @param left the cubic curve object for storing the left or first half of the subdivided curve
   * @param right the cubic curve object for storing the right or second half of the subdivided
   * curve
   * @since 1.2
   */
  public static void subdivide(CubicCurve2D src,
      CubicCurve2D left,
      CubicCurve2D right) {
    double x1 = src.getX1();
    double y1 = src.getY1();
    double ctrlx1 = src.getCtrlX1();
    double ctrly1 = src.getCtrlY1();
    double ctrlx2 = src.getCtrlX2();
    double ctrly2 = src.getCtrlY2();
    double x2 = src.getX2();
    double y2 = src.getY2();
    double centerx = (ctrlx1 + ctrlx2) / 2.0;
    double centery = (ctrly1 + ctrly2) / 2.0;
    ctrlx1 = (x1 + ctrlx1) / 2.0;
    ctrly1 = (y1 + ctrly1) / 2.0;
    ctrlx2 = (x2 + ctrlx2) / 2.0;
    ctrly2 = (y2 + ctrly2) / 2.0;
    double ctrlx12 = (ctrlx1 + centerx) / 2.0;
    double ctrly12 = (ctrly1 + centery) / 2.0;
    double ctrlx21 = (ctrlx2 + centerx) / 2.0;
    double ctrly21 = (ctrly2 + centery) / 2.0;
    centerx = (ctrlx12 + ctrlx21) / 2.0;
    centery = (ctrly12 + ctrly21) / 2.0;
    if (left != null) {
      left.setCurve(x1, y1, ctrlx1, ctrly1,
          ctrlx12, ctrly12, centerx, centery);
    }
    if (right != null) {
      right.setCurve(centerx, centery, ctrlx21, ctrly21,
          ctrlx2, ctrly2, x2, y2);
    }
  }

  /**
   * Subdivides the cubic curve specified by the coordinates
   * stored in the <code>src</code> array at indices <code>srcoff</code>
   * through (<code>srcoff</code>&nbsp;+&nbsp;7) and stores the
   * resulting two subdivided curves into the two result arrays at the
   * corresponding indices.
   * Either or both of the <code>left</code> and <code>right</code>
   * arrays may be <code>null</code> or a reference to the same array
   * as the <code>src</code> array.
   * Note that the last point in the first subdivided curve is the
   * same as the first point in the second subdivided curve. Thus,
   * it is possible to pass the same array for <code>left</code>
   * and <code>right</code> and to use offsets, such as <code>rightoff</code>
   * equals (<code>leftoff</code> + 6), in order
   * to avoid allocating extra storage for this common point.
   *
   * @param src the array holding the coordinates for the source curve
   * @param srcoff the offset into the array of the beginning of the the 6 source coordinates
   * @param left the array for storing the coordinates for the first half of the subdivided curve
   * @param leftoff the offset into the array of the beginning of the the 6 left coordinates
   * @param right the array for storing the coordinates for the second half of the subdivided curve
   * @param rightoff the offset into the array of the beginning of the the 6 right coordinates
   * @since 1.2
   */
  public static void subdivide(double src[], int srcoff,
      double left[], int leftoff,
      double right[], int rightoff) {
    double x1 = src[srcoff + 0];
    double y1 = src[srcoff + 1];
    double ctrlx1 = src[srcoff + 2];
    double ctrly1 = src[srcoff + 3];
    double ctrlx2 = src[srcoff + 4];
    double ctrly2 = src[srcoff + 5];
    double x2 = src[srcoff + 6];
    double y2 = src[srcoff + 7];
    if (left != null) {
      left[leftoff + 0] = x1;
      left[leftoff + 1] = y1;
    }
    if (right != null) {
      right[rightoff + 6] = x2;
      right[rightoff + 7] = y2;
    }
    x1 = (x1 + ctrlx1) / 2.0;
    y1 = (y1 + ctrly1) / 2.0;
    x2 = (x2 + ctrlx2) / 2.0;
    y2 = (y2 + ctrly2) / 2.0;
    double centerx = (ctrlx1 + ctrlx2) / 2.0;
    double centery = (ctrly1 + ctrly2) / 2.0;
    ctrlx1 = (x1 + centerx) / 2.0;
    ctrly1 = (y1 + centery) / 2.0;
    ctrlx2 = (x2 + centerx) / 2.0;
    ctrly2 = (y2 + centery) / 2.0;
    centerx = (ctrlx1 + ctrlx2) / 2.0;
    centery = (ctrly1 + ctrly2) / 2.0;
    if (left != null) {
      left[leftoff + 2] = x1;
      left[leftoff + 3] = y1;
      left[leftoff + 4] = ctrlx1;
      left[leftoff + 5] = ctrly1;
      left[leftoff + 6] = centerx;
      left[leftoff + 7] = centery;
    }
    if (right != null) {
      right[rightoff + 0] = centerx;
      right[rightoff + 1] = centery;
      right[rightoff + 2] = ctrlx2;
      right[rightoff + 3] = ctrly2;
      right[rightoff + 4] = x2;
      right[rightoff + 5] = y2;
    }
  }

  /**
   * Solves the cubic whose coefficients are in the <code>eqn</code>
   * array and places the non-complex roots back into the same array,
   * returning the number of roots.  The solved cubic is represented
   * by the equation:
   * <pre>
   *     eqn = {c, b, a, d}
   *     dx^3 + ax^2 + bx + c = 0
   * </pre>
   * A return value of -1 is used to distinguish a constant equation
   * that might be always 0 or never 0 from an equation that has no
   * zeroes.
   *
   * @param eqn an array containing coefficients for a cubic
   * @return the number of roots, or -1 if the equation is a constant.
   * @since 1.2
   */
  public static int solveCubic(double eqn[]) {
    return solveCubic(eqn, eqn);
  }

  /**
   * Solve the cubic whose coefficients are in the <code>eqn</code>
   * array and place the non-complex roots into the <code>res</code>
   * array, returning the number of roots.
   * The cubic solved is represented by the equation:
   * eqn = {c, b, a, d}
   * dx^3 + ax^2 + bx + c = 0
   * A return value of -1 is used to distinguish a constant equation,
   * which may be always 0 or never 0, from an equation which has no
   * zeroes.
   *
   * @param eqn the specified array of coefficients to use to solve the cubic equation
   * @param res the array that contains the non-complex roots resulting from the solution of the
   * cubic equation
   * @return the number of roots, or -1 if the equation is a constant
   * @since 1.3
   */
  public static int solveCubic(double eqn[], double res[]) {
    // From Graphics Gems:
    // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
    final double d = eqn[3];
    if (d == 0) {
      return QuadCurve2D.solveQuadratic(eqn, res);
    }

        /* normal form: x^3 + Ax^2 + Bx + C = 0 */
    final double A = eqn[2] / d;
    final double B = eqn[1] / d;
    final double C = eqn[0] / d;

    //  substitute x = y - A/3 to eliminate quadratic term:
    //     x^3 +Px + Q = 0
    //
    // Since we actually need P/3 and Q/2 for all of the
    // calculations that follow, we will calculate
    // p = P/3
    // q = Q/2
    // instead and use those values for simplicity of the code.
    double sq_A = A * A;
    double p = 1.0 / 3 * (-1.0 / 3 * sq_A + B);
    double q = 1.0 / 2 * (2.0 / 27 * A * sq_A - 1.0 / 3 * A * B + C);

        /* use Cardano's formula */

    double cb_p = p * p * p;
    double D = q * q + cb_p;

    final double sub = 1.0 / 3 * A;

    int num;
    if (D < 0) { /* Casus irreducibilis: three real solutions */
      // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
      double phi = 1.0 / 3 * Math.acos(-q / Math.sqrt(-cb_p));
      double t = 2 * Math.sqrt(-p);

      if (res == eqn) {
        eqn = Arrays.copyOf(eqn, 4);
      }

      res[0] = (t * Math.cos(phi));
      res[1] = (-t * Math.cos(phi + Math.PI / 3));
      res[2] = (-t * Math.cos(phi - Math.PI / 3));
      num = 3;

      for (int i = 0; i < num; ++i) {
        res[i] -= sub;
      }

    } else {
      // Please see the comment in fixRoots marked 'XXX' before changing
      // any of the code in this case.
      double sqrt_D = Math.sqrt(D);
      double u = Math.cbrt(sqrt_D - q);
      double v = -Math.cbrt(sqrt_D + q);
      double uv = u + v;

      num = 1;

      double err = 1200000000 * ulp(abs(uv) + abs(sub));
      if (iszero(D, err) || within(u, v, err)) {
        if (res == eqn) {
          eqn = Arrays.copyOf(eqn, 4);
        }
        res[1] = -(uv / 2) - sub;
        num = 2;
      }
      // this must be done after the potential Arrays.copyOf
      res[0] = uv - sub;
    }

    if (num > 1) { // num == 3 || num == 2
      num = fixRoots(eqn, res, num);
    }
    if (num > 2 && (res[2] == res[1] || res[2] == res[0])) {
      num--;
    }
    if (num > 1 && res[1] == res[0]) {
      res[1] = res[--num]; // Copies res[2] to res[1] if needed
    }
    return num;
  }

  // preconditions: eqn != res && eqn[3] != 0 && num > 1
  // This method tries to improve the accuracy of the roots of eqn (which
  // should be in res). It also might eliminate roots in res if it decideds
  // that they're not real roots. It will not check for roots that the
  // computation of res might have missed, so this method should only be
  // used when the roots in res have been computed using an algorithm
  // that never underestimates the number of roots (such as solveCubic above)
  private static int fixRoots(double[] eqn, double[] res, int num) {
    double[] intervals = {eqn[1], 2 * eqn[2], 3 * eqn[3]};
    int critCount = QuadCurve2D.solveQuadratic(intervals, intervals);
    if (critCount == 2 && intervals[0] == intervals[1]) {
      critCount--;
    }
    if (critCount == 2 && intervals[0] > intervals[1]) {
      double tmp = intervals[0];
      intervals[0] = intervals[1];
      intervals[1] = tmp;
    }

    // below we use critCount to possibly filter out roots that shouldn't
    // have been computed. We require that eqn[3] != 0, so eqn is a proper
    // cubic, which means that its limits at -/+inf are -/+inf or +/-inf.
    // Therefore, if critCount==2, the curve is shaped like a sideways S,
    // and it could have 1-3 roots. If critCount==0 it is monotonic, and
    // if critCount==1 it is monotonic with a single point where it is
    // flat. In the last 2 cases there can only be 1 root. So in cases
    // where num > 1 but critCount < 2, we eliminate all roots in res
    // except one.

    if (num == 3) {
      double xe = getRootUpperBound(eqn);
      double x0 = -xe;

      Arrays.sort(res, 0, num);
      if (critCount == 2) {
        // this just tries to improve the accuracy of the computed
        // roots using Newton's method.
        res[0] = refineRootWithHint(eqn, x0, intervals[0], res[0]);
        res[1] = refineRootWithHint(eqn, intervals[0], intervals[1], res[1]);
        res[2] = refineRootWithHint(eqn, intervals[1], xe, res[2]);
        return 3;
      } else if (critCount == 1) {
        // we only need fx0 and fxe for the sign of the polynomial
        // at -inf and +inf respectively, so we don't need to do
        // fx0 = solveEqn(eqn, 3, x0); fxe = solveEqn(eqn, 3, xe)
        double fxe = eqn[3];
        double fx0 = -fxe;

        double x1 = intervals[0];
        double fx1 = solveEqn(eqn, 3, x1);

        // if critCount == 1 or critCount == 0, but num == 3 then
        // something has gone wrong. This branch and the one below
        // would ideally never execute, but if they do we can't know
        // which of the computed roots is closest to the real root;
        // therefore, we can't use refineRootWithHint. But even if
        // we did know, being here most likely means that the
        // curve is very flat close to two of the computed roots
        // (or maybe even all three). This might make Newton's method
        // fail altogether, which would be a pain to detect and fix.
        // This is why we use a very stable bisection method.
        if (oppositeSigns(fx0, fx1)) {
          res[0] = bisectRootWithHint(eqn, x0, x1, res[0]);
        } else if (oppositeSigns(fx1, fxe)) {
          res[0] = bisectRootWithHint(eqn, x1, xe, res[2]);
        } else /* fx1 must be 0 */ {
          res[0] = x1;
        }
        // return 1
      } else if (critCount == 0) {
        res[0] = bisectRootWithHint(eqn, x0, xe, res[1]);
        // return 1
      }
    } else if (num == 2 && critCount == 2) {
      // XXX: here we assume that res[0] has better accuracy than res[1].
      // This is true because this method is only used from solveCubic
      // which puts in res[0] the root that it would compute anyway even
      // if num==1. If this method is ever used from any other method, or
      // if the solveCubic implementation changes, this assumption should
      // be reevaluated, and the choice of goodRoot might have to become
      // goodRoot = (abs(eqn'(res[0])) > abs(eqn'(res[1]))) ? res[0] : res[1]
      // where eqn' is the derivative of eqn.
      double goodRoot = res[0];
      double badRoot = res[1];
      double x1 = intervals[0];
      double x2 = intervals[1];
      // If a cubic curve really has 2 roots, one of those roots must be
      // at a critical point. That can't be goodRoot, so we compute x to
      // be the farthest critical point from goodRoot. If there are two
      // roots, x must be the second one, so we evaluate eqn at x, and if
      // it is zero (or close enough) we put x in res[1] (or badRoot, if
      // |solveEqn(eqn, 3, badRoot)| < |solveEqn(eqn, 3, x)| but this
      // shouldn't happen often).
      double x = abs(x1 - goodRoot) > abs(x2 - goodRoot) ? x1 : x2;
      double fx = solveEqn(eqn, 3, x);

      if (iszero(fx, 10000000 * ulp(x))) {
        double badRootVal = solveEqn(eqn, 3, badRoot);
        res[1] = abs(badRootVal) < abs(fx) ? badRoot : x;
        return 2;
      }
    } // else there can only be one root - goodRoot, and it is already in res[0]

    return 1;
  }

  // use newton's method.
  private static double refineRootWithHint(double[] eqn, double min, double max, double t) {
    if (!inInterval(t, min, max)) {
      return t;
    }
    double[] deriv = {eqn[1], 2 * eqn[2], 3 * eqn[3]};
    double origt = t;
    for (int i = 0; i < 3; i++) {
      double slope = solveEqn(deriv, 2, t);
      double y = solveEqn(eqn, 3, t);
      double delta = -(y / slope);
      double newt = t + delta;

      if (slope == 0 || y == 0 || t == newt) {
        break;
      }

      t = newt;
    }
    if (within(t, origt, 1000 * ulp(origt)) && inInterval(t, min, max)) {
      return t;
    }
    return origt;
  }

  private static double bisectRootWithHint(double[] eqn, double x0, double xe, double hint) {
    double delta1 = Math.min(abs(hint - x0) / 64, 0.0625);
    double delta2 = Math.min(abs(hint - xe) / 64, 0.0625);
    double x02 = hint - delta1;
    double xe2 = hint + delta2;
    double fx02 = solveEqn(eqn, 3, x02);
    double fxe2 = solveEqn(eqn, 3, xe2);
    while (oppositeSigns(fx02, fxe2)) {
      if (x02 >= xe2) {
        return x02;
      }
      x0 = x02;
      xe = xe2;
      delta1 /= 64;
      delta2 /= 64;
      x02 = hint - delta1;
      xe2 = hint + delta2;
      fx02 = solveEqn(eqn, 3, x02);
      fxe2 = solveEqn(eqn, 3, xe2);
    }
    if (fx02 == 0) {
      return x02;
    }
    if (fxe2 == 0) {
      return xe2;
    }

    return bisectRoot(eqn, x0, xe);
  }

  private static double bisectRoot(double[] eqn, double x0, double xe) {
    double fx0 = solveEqn(eqn, 3, x0);
    double m = x0 + (xe - x0) / 2;
    while (m != x0 && m != xe) {
      double fm = solveEqn(eqn, 3, m);
      if (fm == 0) {
        return m;
      }
      if (oppositeSigns(fx0, fm)) {
        xe = m;
      } else {
        fx0 = fm;
        x0 = m;
      }
      m = x0 + (xe - x0) / 2;
    }
    return m;
  }

  private static boolean inInterval(double t, double min, double max) {
    return min <= t && t <= max;
  }

  private static boolean within(double x, double y, double err) {
    double d = y - x;
    return (d <= err && d >= -err);
  }

  private static boolean iszero(double x, double err) {
    return within(x, 0, err);
  }

  private static boolean oppositeSigns(double x1, double x2) {
    return (x1 < 0 && x2 > 0) || (x1 > 0 && x2 < 0);
  }

  private static double solveEqn(double eqn[], int order, double t) {
    double v = eqn[order];
    while (--order >= 0) {
      v = v * t + eqn[order];
    }
    return v;
  }

  /*
   * Computes M+1 where M is an upper bound for all the roots in of eqn.
   * See: http://en.wikipedia.org/wiki/Sturm%27s_theorem#Applications.
   * The above link doesn't contain a proof, but I [dlila] proved it myself
   * so the result is reliable. The proof isn't difficult, but it's a bit
   * long to include here.
   * Precondition: eqn must represent a cubic polynomial
   */
  private static double getRootUpperBound(double[] eqn) {
    double d = eqn[3];
    double a = eqn[2];
    double b = eqn[1];
    double c = eqn[0];

    double M = 1 + max(max(abs(a), abs(b)), abs(c)) / abs(d);
    M += ulp(M) + 1;
    return M;
  }


  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(double x, double y) {
    if (!(x * 0.0 + y * 0.0 == 0.0)) {
            /* Either x or y was infinite or NaN.
             * A NaN always produces a negative response to any test
             * and Infinity values cannot be "inside" any path so
             * they should return false as well.
             */
      return false;
    }
    // We count the "Y" crossings to determine if the point is
    // inside the curve bounded by its closing line.
    double x1 = getX1();
    double y1 = getY1();
    double x2 = getX2();
    double y2 = getY2();
    int crossings =
        (Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
            Curve.pointCrossingsForCubic(x, y,
                x1, y1,
                getCtrlX1(), getCtrlY1(),
                getCtrlX2(), getCtrlY2(),
                x2, y2, 0));
    return ((crossings & 1) == 1);
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(Point2D p) {
    return contains(p.getX(), p.getY());
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean intersects(double x, double y, double w, double h) {
    // Trivially reject non-existant rectangles
    if (w <= 0 || h <= 0) {
      return false;
    }

    int numCrossings = rectCrossings(x, y, w, h);
    // the intended return value is
    // numCrossings != 0 || numCrossings == Curve.RECT_INTERSECTS
    // but if (numCrossings != 0) numCrossings == INTERSECTS won't matter
    // and if !(numCrossings != 0) then numCrossings == 0, so
    // numCrossings != RECT_INTERSECT
    return numCrossings != 0;
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean intersects(Rectangle2D r) {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(double x, double y, double w, double h) {
    if (w <= 0 || h <= 0) {
      return false;
    }

    int numCrossings = rectCrossings(x, y, w, h);
    return !(numCrossings == 0 || numCrossings == Curve.RECT_INTERSECTS);
  }

  private int rectCrossings(double x, double y, double w, double h) {
    int crossings = 0;
    if (!(getX1() == getX2() && getY1() == getY2())) {
      crossings = Curve.rectCrossingsForLine(crossings,
          x, y,
          x + w, y + h,
          getX1(), getY1(),
          getX2(), getY2());
      if (crossings == Curve.RECT_INTERSECTS) {
        return crossings;
      }
    }
    // we call this with the curve's direction reversed, because we wanted
    // to call rectCrossingsForLine first, because it's cheaper.
    return Curve.rectCrossingsForCubic(crossings,
        x, y,
        x + w, y + h,
        getX2(), getY2(),
        getCtrlX2(), getCtrlY2(),
        getCtrlX1(), getCtrlY1(),
        getX1(), getY1(), 0);
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public boolean contains(Rectangle2D r) {
    return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * {@inheritDoc}
   *
   * @since 1.2
   */
  public Rectangle getBounds() {
    return getBounds2D().getBounds();
  }

  /**
   * Returns an iteration object that defines the boundary of the
   * shape.
   * The iterator for this class is not multi-threaded safe,
   * which means that this <code>CubicCurve2D</code> class does not
   * guarantee that modifications to the geometry of this
   * <code>CubicCurve2D</code> object do not affect any iterations of
   * that geometry that are already in process.
   *
   * @param at an optional <code>AffineTransform</code> to be applied to the coordinates as they are
   * returned in the iteration, or <code>null</code> if untransformed coordinates are desired
   * @return the <code>PathIterator</code> object that returns the geometry of the outline of this
   * <code>CubicCurve2D</code>, one segment at a time.
   * @since 1.2
   */
  public PathIterator getPathIterator(AffineTransform at) {
    return new CubicIterator(this, at);
  }

  /**
   * Return an iteration object that defines the boundary of the
   * flattened shape.
   * The iterator for this class is not multi-threaded safe,
   * which means that this <code>CubicCurve2D</code> class does not
   * guarantee that modifications to the geometry of this
   * <code>CubicCurve2D</code> object do not affect any iterations of
   * that geometry that are already in process.
   *
   * @param at an optional <code>AffineTransform</code> to be applied to the coordinates as they are
   * returned in the iteration, or <code>null</code> if untransformed coordinates are desired
   * @param flatness the maximum amount that the control points for a given curve can vary from
   * colinear before a subdivided curve is replaced by a straight line connecting the end points
   * @return the <code>PathIterator</code> object that returns the geometry of the outline of this
   * <code>CubicCurve2D</code>, one segment at a time.
   * @since 1.2
   */
  public PathIterator getPathIterator(AffineTransform at, double flatness) {
    return new FlatteningPathIterator(getPathIterator(at), flatness);
  }

  /**
   * Creates a new object of the same class as this object.
   *
   * @return a clone of this instance.
   * @throws OutOfMemoryError if there is not enough memory.
   * @see java.lang.Cloneable
   * @since 1.2
   */
  public Object clone() {
    try {
      return super.clone();
    } catch (CloneNotSupportedException e) {
      // this shouldn't happen, since we are Cloneable
      throw new InternalError(e);
    }
  }
}
